On the infinitesimal dispersion of multivariate Markov counting systems |
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| Authors: | Carles Bretó |
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| Affiliation: | Departamento de Estadística and Instituto Flores de Lemus, Universidad Carlos III de Madrid, C/ Madrid 126, Getafe, Madrid 28903, Spain |
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| Abstract: | We provide a multivariate extension of a recent result for univariate Markov counting processes: necessity and sufficiency of compoundness for infinitesimal over-dispersion. As an illustration, we show that infinitesimally over-dispersed epidemiological SIR-type compartment models must rely on compound counting processes. |
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| Keywords: | Multivariate infinitesimal over-dispersion Continuous-time Markov chain Compound process Compartment model |
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